Pengcheng Hao

Pengcheng Hao, Huaze Tang, Ercan Engin Kuruoglu et al.

Bayesian deep learning (BDL) provides a principled framework for reliable uncertainty quantification by combining deep neural networks with Bayesian inference. A central challenge in BDL lies in the design of informative prior distributions that scale effectively to high-dimensional data. Recent functional variational inference (VI) approaches address this issue by imposing priors directly in function space; however, most existing methods rely on Gaussian process (GP) priors, whose expressiveness and generalisation capabilities become limited in high-dimensional regimes. In this work, we propose VLM-FS-EB, a novel function-space empirical Bayes regularisation framework, leveraging large vision-language models (VLMs) to generates semantically meaningful context points. These synthetic samples are then used VLMs for embeddings to construct expressive functional priors. Furthermore, the proposed method is evaluated against various baselines, and experimental results demonstrate that our method consistently improves predictive performance and yields more reliable uncertainty estimates, particularly in out-of-distribution (OOD) detection tasks and data-scarce regimes.

Pengcheng Hao, Ercan Engin Kuruoglu

Bayesian deep learning (BDL) has emerged as a principled approach to produce reliable uncertainty estimates by integrating deep neural networks with Bayesian inference, and the selection of informative prior distributions remains a significant challenge. Various function-space variational inference (FSVI) regularisation methods have been presented, assigning meaningful priors over model predictions. However, these methods typically rely on a Gaussian prior, which fails to capture the heavy-tailed statistical characteristics inherent in neural network outputs. By contrast, this work proposes a novel function-space empirical Bayes regularisation framework -- termed ST-FS-EB -- which employs heavy-tailed Student's $t$ priors in both parameter and function spaces. Also, we approximate the posterior distribution through variational inference (VI), inducing an evidence lower bound (ELBO) objective based on Monte Carlo (MC) dropout. Furthermore, the proposed method is evaluated against various VI-based BDL baselines, and the results demonstrate its robust performance in in-distribution prediction, out-of-distribution (OOD) detection and handling distribution shifts.

Pengcheng Hao, Menghao Waiyan William Zhu, Ercan Engin Kuruoglu

Continual learning (CL) is crucial for the adaptation of neural network models to new environments. Although outperforming weight-space regularisation approaches, the functional regularisation-based CL methods suffer from high computational costs and large linear approximation errors. In this work, we present a new functional regularisation CL framework, called MCFRCL, which approximates model prediction distributions by Monte Carlo (MC) sampling. Moreover, three continuous distributions are leveraged to capture the statistical characteristics of the MC samples via moment-based methods. Additionally, both the Wasserstein distance and the Kullback-Leibler (KL) distance are employed to construct the regularisation function. The proposed MCFRCL is evaluated against multiple benchmark methods on the MNIST and CIFAR datasets, with simulation results highlighting its effectiveness in both prediction accuracy and training efficiency.

Menghao Waiyan William Zhu, Pengcheng Hao, Ercan Engin Kuruoğlu

Continual learning in neural networks aims to learn new tasks without forgetting old tasks. Sequential function-space variational inference (SFSVI) uses a Gaussian variational distribution to approximate the distribution of the outputs of the neural network corresponding to a finite number of selected inducing points. Since the posterior distribution of a neural network is multi-modal, a Gaussian distribution could only match one mode of the posterior distribution, and a Gaussian mixture distribution could be used to better approximate the posterior distribution. We propose an SFSVI method based on a Gaussian mixture variational distribution. We also compare different types of variational inference methods with a fixed pre-trained feature extractor (where continual learning is performed on the final layer) and without a fixed pre-trained feature extractor (where continual learning is performed on all layers). We find that in terms of final average accuracy, likelihood-focused Gaussian mixture SFSVI outperforms other sequential variational inference methods, especially in the latter case.